Answers
Answer:
-11
Step-by-step explanation:
f(x) = 5x + 11
g(x) = x^2 + 4x - 11
g(f(-3)) = ?
f(-3) = 5(-3) + 11
= -15 + 11 = -4
g(f(-3)) = g(-4) = -(4)^2 + 4(-4) - 11
= 16 - 16 - 11 = -11
A function assigns the value of each element of one set to the other specific element of another set. The value of g(f(-3)) is -11.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given f(x)=5x+11 and g(x)=x²+4x-11, therefore, we can write the value of g(f(x)) as,
g(f(x)) = (5x + 11)² + 4(5x + 11) - 11
= 25x² + 121 + 110x + 20x + 44 - 11
= 25x² + 130x + 154
Now, substitute the value of x as -3 in the function g(f(x)), therefore, we can write,
g(f(-3)) = 25x² + 130x + 154
= 25(3)² + 130(-3) + 154
= 225 - 390 + 154
= -11
Hence, the value of g(f(-3)) is -11.
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Related Questions
(5x+6) over 2 = 3 (4x+12)
Answers
x= -66/19
Multiply 2 on both sides:
2*(5x+6)/2=3(4x+12)*2
Simplify:
5x+6=24x+72
Subtract 6 from both sides:
5x+6-6=24x+72-6
Simplify:
5x=24x+66
Subtract 24x from both sides:
5x-24x=24x+66-24x
Simplify:
-19x=66
Divide both sides by -19
-19x/-19=66/-19
Simplify:
x= -66/19
Write 1/4x-3/4y=-1 in standard form
work out
need asap
please
Answers
YALL COME PLAY WITH ME AMONG US ZSFNQQ
Answers
Answer:
OK lets do it
Step-by-step explanation:
Answer:
What?
Step-by-step explanation:
There are 49 female performers in a dance recital. The ratio of men to women is 5:7. How many men are in the dance recital?
Answers
Answer:
35 Men were in the dance recital
Step-by-step explanation:
The ratio from MEN to WOMEN is 5:7
49 female performers is 7
49/7= 7 performers
to find how many men, you would do 7*5
7*5= 35
35 Men were in the dance recital
Hope this helps and made sense!
Triangle FGH is graphed on the coordinate plane below.
On a coordinate plane, triangle F G H has points (negative 6, negative 8), (negative 2, negative 3), (negative 4, negative 2).
The figure is rotated 180° using the origin as the center of rotation. How do the coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image?
(x, y) right-arrow (y, x)
(x, y) right-arrow (negative y, negative x)
(x, y) right-arrow (negative x, negative y)
(x, y) right-arrow (x, negative y)
Answers
Answer:
(x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
Step-by-step explanation:
Let us revise the rotation about the origin
If point (x, y) rotated about the origin by angle 90° counterclockwise (or 270° clockwise), then its image is (-y, x) . The rule is (x, y) → (-y, x)If point (x, y) rotated about the origin by angle 180° counterclockwise ( or 180° clockwise), then its image is (-x, -y) . The rule is (x, y) → (-x, -y)If point (x, y) rotated about the origin by angle 270° counterclockwise (90° clockwise), then its image is (y, -x) . The rule is (x, y) → (y, -x)Let us solve the question
∵ The vertices of triangle FGH are (-6, -8), (-2, -3), (-4, -2)
∵ The figure is rotated 180° using the origin as the center of rotation
→ By using the 2nd rule above
∴ The vertices of its image are (6, 8), (2, 3), (4, 2)
∴ The rule is (x, y) → (-x, -y)
The coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image do (x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
Answer:
B. they over explaining
Step-by-step explanation:
1, 2, 3, 5, 8, ____, ____, ____ Give the next three numbers in the pattern.
Answers
Answer: 10, 12, 14 are the next numbers
Explanation:
If f(2) = 22 – 5, then what is the value of f(2) + f(5)?
Answers
Answer:
67
Step-by-step explanation:
With the information of f(2) = 22-5, you can assume the equation will be f(x) = 11x-5. Using this, you can calculate f(5) by doing 11(5)-5, which is 50. 22-5 is 17, so 50+17=67
Which expression is equivalent to
Answers
Answer:
a
Step-by-step explanation:
how can you get 6 with four 6s , the problem is
6 6 6 6 equals 6
Answers
Answer:
6666 divided by 1111 equals 6
Step-by-step explanation:
7-14m=2m=5 please help
Answers
Answer:
M=1/6
Step-by-step explanation:
What is the answer?
Answers
Hope this helps
Solve using the Quadratic Formula. 3x2 - 7x - 3 = 0
Answers
Answer:
[tex]\displaystyle x_1=\frac{7+ \sqrt{85}}{6}\approx 2.70\\\displaystyle x_2=\frac{7- \sqrt{85}}{6}\approx -0.37[/tex]
Step-by-step explanation:
Quadratic Formula
Given the second-degree equation:
[tex]ax^2+bx+c=0[/tex]
The solutions of the equation can be obtained by applying the formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The equation to solve is:
[tex]3x^2-7x-3=0[/tex]
Which means the values of the coefficients are: a=3, b=-7, c=-3. Substituting the values in the formula:
[tex]\displaystyle x=\frac{-(-7)\pm \sqrt{(-7)^2-4(3)(-3)}}{2(3)}[/tex]
[tex]\displaystyle x=\frac{7\pm \sqrt{49+36}}{6}[/tex]
[tex]\displaystyle x=\frac{7\pm \sqrt{85}}{6}[/tex]
There are two real solutions for this equation:
[tex]\displaystyle x_1=\frac{7+ \sqrt{85}}{6}[/tex]
[tex]\displaystyle x_2=\frac{7- \sqrt{85}}{6}[/tex]
The approximate values of both roots are:
[tex]x_1\approx 2.70[/tex]
[tex]x_2\approx -0.37[/tex]
PLZ HELP! The equation is 7d+3n=85.
Answers
Answer:
Step-by-step explanation:
[tex]7d + 3n = 85 \\ 7d = 85 - 3n\\d = \frac{85}{7} - \frac{3}{7}x\\\\[/tex]
The slope of the equation is -3/7 and the y-intercept is 85/7
The table shows values for the two functions f and g for different values of x.
What is f(g(0))?
-1
0
1
This composition is undefined.
Answers
Answer:
C.) 1
Step-by-step explanation:
EDG 2020
The value of f(g(0)) is 1.
What is Composition of Functions?Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).
h(x) is called the composite function.
Given a table which shows values for the two functions f and g for different values of x.
We have to find the value of f(g(0)).
f(g(0)) = f[ g(0)]
From the table, g(0) = -1.
f(g(0)) = f(-1) = 1
Hence the value of f(g(0)) is 1.
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The table is given below.
The longest leg of a right triangle is 30 feet and another side is 20 feet. Find the perimeter of the triangle. Round to the nearest tenth
Answers
Answer: 72.4 ft
Step-by-step explanation: A2+B2=C2 20squared plus Bsquared=30 22.4 squared plus 20squared equals 30squared and when you add all that together you get 72.4 ft
An observation deck extends 199 feet out above a valley. The deck sits 149 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h= -16t^2+149. How long will it take for the object to be 5 feet above the valley floor?
Answers
Answer:
Step-by-step explanation:
Give the height of the observation deck modeled by the equation
h= -16t^2+149 where t is in seconds;
To get the time it will take the object to be 5 feet above the valley floor, we wil substitute h = 5ft into the modeled equation and calculate t;
h= -16t^2+149
5= -16t^2+149
-16t^2 = 5-149
-16t^2 = -144
t² = 144/16
t² = 9
t = √9
t = 3secs
Hence the time it will take for the object to be 5 feet above the valley floor is 3secs
2.1 ÷ 1.488 rounded to the nearest tenth, I will Give you 20 Points
Answers
If the number is above 5, you round to the next highest number.
If the number is 4 and below, you don’t round to the next highest number.
Since 1.41 has a number below 4 that you have to round, the nearest tenth would stay 4.
meaning the answer is 1.4
X + 5 = 1
—
4. Step by step please help!!!
Answers
Answer: x=-8
Step-by-step explanation:
X+5=1-4
X+5=-3
Now subtract 5 from both sides
X=-8
X+5=1
-5. -5. ( subtract 5 from both sides)
_________
X = -4 ( 1-5=-4)
[48(72-12)-15] divided by 9
Answers
Answer:
318.33...
Step-by-step explanation:
[48(60)-15]/9
[2880-15]/9
2865/9
318.33
Answer:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
955/3
Decimal Form:
318.¯3(repeating)
Mixed Number Form:
318 1/3
Hope this helps :)
Akiko wants to fence in her [tex]12[/tex] ft by [tex]10[/tex] ft vegetable garden. There will be a path [tex]x[/tex] ft wide between the garden and the fence. The area to be enclosed by the fence will be [tex]360[/tex] sq ft. Write a quadratic function that can be used to determine the value of [tex]x[/tex].
Answers
Answer:
see below
Step-by-step explanation:
The length is 12 + 2x and the width is 10 + 2x
A = l*w
360 = ( 12+2x) ( 10+2x)
FOIL
360 = 120 + 24x+20x + 4x^2
Combine like terms
360 = 4x^2 +44x+120
Subtract 360 from each side
0 = 4x^2 +44x +120-360
0 = 4x^2+ 44x -240
For fun, lets solve
0 = 4( x^2 + 11x - 60)
0 = 4( x+15) ( x-4)
Using the zero product property
x= -15 x=4
Since we cannot have negative length
x=4 ft
Answer:
[tex]x^2+11x-60=0[/tex]
Step-by-step explanation:
Refer to the drawing.
We know that the area enclosed by the fence is 360 square feet. Remember that the area for a rectangle is given by the following formula:
[tex]A=bh[/tex]
So, let's substitute 360 for A, (12+2x) for b, and (10+2x) for h. This yields:
[tex]360=(12+2x)(10+2x)[/tex]
We can simplify this. On the right, factor out a 2 from the first term and a 2 from the second. This yields:
[tex]360=2(6+x)\cdot2(5+x)[/tex]
Multiply:
[tex]360=4(x+6)(x+5)[/tex]
Divide both sides by 4:
[tex]90=(x+6)(x+5)[/tex]
Multiply on the right:
[tex]90=x^2+6x+5x+30[/tex]
Add on the right:
[tex]90=x^2+11x+30[/tex]
Subtract 90 from both sides. So, our equation is:
[tex]x^2+11x-60=0[/tex]
And we're done!
Chris wants to order DVDS over the internet. Each DVD costs $ 15.99 and shipping for the entire order is $ 9.99. How much will Chris spend (s) if he buys x DVDS?
Answers
Answer:
There are 3 DVD s that can be bought with under $100.
Step-by-step explanation:
Since we have given that
Cost of DVD = $15.99
Cost of Shipping = $ 9.99
Total cost per DVD would be
$15.99 + $9.99 = $ 25.98
Amount he has to spend no more than $ 100.
So, number of DVDs would be
100 ÷ 25.98 = 3.84
Hence, there are 3 DVD s that can be bought with under $100.
Edwin and Anthony are building a rectangular deck in their backyard. The longer side is 2 ft more than 1/3 of the perimeter. The shorter side is 1/10 of the perimeter. They also know that the longer side is 9 ft longer than the shorter side. What is the perimeter of the deck?
Answers
Answer:
30 ft
Step-by-step explanation:
Perimeter of a rectangle = 2(length + width)
Let
Perimeter = x
Length = 1/3x + 2
Width = 1/10x
Length = 9 + 1/10x
Perimeter of the deck = 2(length + width)
x = 2(1/3x + 2 + 1/10x)
x = 2(10x+3x/30 + 2)
x = 2(13/30x + 2)
x = 26/30x + 4
x - 26/30x = 4
30x-26x/30 = 4
4/30x = 4
Divide both sides by 4/30
x = 4 ÷ 4/30
= 4 × 30/4
x = 30 ft
Length = 1/3x + 2
= 1/3(30) + 2
= 30/3 + 2
= 10 + 2
= 12 ft
Width = 1/10x
= 1/10(30)
= 30/10
= 3 ft
Length = 9 + 1/10x
= 9 + 1/10(30)
= 9 + 30/10
= 9 + 3
= 12 ft
The perimeter of the deck = x = 30 ft
Given the function:
f (x) = (3 x + 4) minus (2 minus x)
Evaluate for f (5).
a.22
b.15
c.16
d.30
Answers
f(5) = (15+4)- (-3)
f(5) = 19+3
f(5) = 22
Answer:
A
Step-by-step explanation:
Given f(x) = 1/3(4-x),What is the value of f(16)?
Answers
Answer:
-1/4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
16f=−4
Step 2: Divide both sides by 16.
if 3 times a number added to 2 is divided by the number plus 9 the result is 5 halves. find the number
Answers
Answer:
2/7
Step-by-step explanation:
What is the equation in slope-intercept form of the line that passes through the points ( -4, 47) and ( 2 , -16)?
A) y= -
21
2
x +
979
21
B) y= -
2
21
x +
979
21
C) y= -
21
2
x + 5
D) y= -
2
21
x +5
Answers
Answer:c
Step-by-step explanation:
is -9/3 a rational number
Answers
Answer:
no
Step-by-step explanation:
Answer: Yes
Step-by-step explanation: The rational numbers include all positive numbers, negative numbers, and zero that can be written as a ratio (fraction) of one number over another. Whole numbers, integers, fractions, terminating decimals, and repeating decimals are all rational numbers.
Someone please help me on this one I don’t know if this is correct
Answers
Answer:
Can you type the choices please?
pretty sure this is right!
What is the solution to the inequality -2(m+3)<4
Answers
Answer:
m>−5
Step-by-step explanation:
Graph the line that passes through the points (3,7) and (-9, -1) and determine
the equation of the line.
Answers
Answer:
y=2/3+5
Step-by-step explanation:
Answer:
y=2/3+5
Step-by-step explanation:
